The Conjugate Linearized Ricci Flow on Closed 3-Manifolds
Abstract
We characterize the conjugate linearized Ricci flow and the associated backward heat kernel on closed three--manifolds of bounded geometry. We discuss their properties, and introduce the notion of Ricci flow conjugated constraint sets which characterizes a way of Ricci flow averaging metric dependent geometrical data. We also provide an integral representation of the Ricci flow metric itself and of its Ricci tensor in terms of the heat kernel of the conjugate linearized Ricci flow. These results, which readily extend to closed n-dimensional manifolds, yield for various conservation laws, monotonicity and asymptotic formulas for the Ricci flow and its linearization.
Keywords
Cite
@article{arxiv.0710.3342,
title = {The Conjugate Linearized Ricci Flow on Closed 3-Manifolds},
author = {Mauro Carfora},
journal= {arXiv preprint arXiv:0710.3342},
year = {2009}
}
Comments
We added a few references and indications of which result extends to n-dimensional manifold. A few complex computations have been presented in full detail. This version of the paper matches the work to appear in Annali della Scuola Normale Superiore di Pisa